The diffusion of interstitial atomic hydrogen in 4H-SiC was investigated theoretically, using the local density approximation of density functional theory. We have found that the diffusion barrier in the perfect crystal is ഛ0.6 eV. Comparing this value with the calculated zero point vibration energy of interstitial hydrogen indicates that hydrogen diffuses very rapidly in perfect portions of the SiC lattice, until it gets trapped. In p-doped (B, Al) material the dissociation of the hydrogen-acceptor complexes is the limiting step in diffusion, with a calculated dissociation energy of 2.5 and 1.6 eV for B + H and Al+ H, respectively. In irradiated material the trapping and detrapping of hydrogen by silicon vacancies determines the effective diffusion barrier, which lies between 4.0 and 5.3 eV depending on the Fermi level in p-type and weakly n-type material.